Atkin-Lehner |
2- 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75504bd |
Isogeny class |
Conductor |
75504 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
-12694557458449152 = -1 · 28 · 315 · 112 · 134 |
Discriminant |
Eigenvalues |
2- 3+ 0 -1 11- 13+ 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-510253,140564833] |
[a1,a2,a3,a4,a6] |
Generators |
[141:8450:1] |
Generators of the group modulo torsion |
j |
-474303061636096000/409819132827 |
j-invariant |
L |
4.606495684832 |
L(r)(E,1)/r! |
Ω |
0.39692383309087 |
Real period |
R |
2.9013725687629 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999125 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
18876g1 75504br1 |
Quadratic twists by: -4 -11 |